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Strong universal consistency of smooth kernel regression estimates |
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| Authors: | Harro Walk |
| Affiliation: | 1. Fachbereich Mathematik, Universit?t Stuttgart, Pfaffenwaldring 57, D-70569, Stuttgart, Germany |
| Abstract: | The paper deals with kernel estimates of Nadaraya-Watson type for a regression function with square integrable response variable. For usual bandwidth sequences and smooth nonnegative kernels, e.g., Gaussian and quartic kernels, strongL 2-consistency is shown without any further condition on the underlying distribution. The proof uses a Tauberian theorem for Cesàro summability. |
| Keywords: | and phrases Nonparametric regression estimation kernel estimate of Nadaraya and Watson square integrability strong and weak universal consistency Efron-Stein inequality covering Tauberian theorem |
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